Question

There are nine judges on the Supreme Court, and for most rulings, a majority is needed. How many combinations of votes are possible for a majority to be reached? (Hint: The majority could be 5, 6, 7, 8, or 9 votes.)

Answer 1

The combinations formula is nCr = $\frac{n!}{r!(n-r)!}$
n = complete value set     r = desired goal
to find combinations we find all combos for 5,6,7,8,and 9 and add them together.
which come out as 126, 84, 36, 9 and 1
Therefore there are 256 combinations